This paper is concerned with the design and control of a tilt-rotor UAV (TRUAV), with the purpose of simplifying the mechanical structure and transition handling. Previous works on TRUAVs control consider a different controller for each flight mode. Furthermore, two sets of actuators are used: propellers in the VTOL mode, and aerodynamic surfaces in the fixed-wing mode. In this work, a new design that does not contain any control surfaces is proposed. A new control strategy is also presented to accommodate this particularity. Unlike previous works, this strategy uses a single controller to handle both flight phases, making the transition between the two phases no longer an issue. Furthermore, such a characteristic makes the drone capable of following any flight trajectory, which is vital for applications such as the tracking of a ground target. Simulations, conducted on the full nonlinear model of the famous Zagi flying wing drone, showed the effectiveness of the proposed control strategy in tracking a typical trajectory profile with a smooth transition from VTOL to fixed-wing mode.